reflections from a cubic lattice

a fingerprint

an X-ray spectrum

 a simulated powder diffraction pattern

7 crystal systems,

14 Bravais lattices and

230 3D space groups.

10 Laue classes,

33 crystal classes and

230 3D space groups.

17 plane groups and

226 space groups

11 Laue classes,

32 crystallographic point groups and

10 Bravais lattices.

They get broader.

They appear further apart.

Their positions on the detector do not change.

They appear closer together.

Sharpness does not require a specific number of repeats.

2 repeats

22 repeats

122 repeats

cm

p2mg

p4mm

p2gg

90°

180°

120°

b* and c* do not intersect.

centrosymmetric.

non-centrosymmetric.

a Sohncke group: enantiopure chiral compounds can crystallize in it.

face-centered.

The reflections for crystal B appear further apart.

The reflections for crystal B appear closer together.

No change.

Crystal B has sharper reflections but less resolution.

was invented by Friedel Ewald around 1925.

relates real and reciprocal space.

is a sphere containing all reflections of a crystal.

is a sphere with r = λ/2.

Å

ų

a.u.

Å^-1

the used X-ray wavelength.

the size of the unit cell.

the arrangement of the contents within the unit cell.

all of the above.

must be the same as in solution.

must be different from the solution.

might or might not be the same as in solution.

is a Boltzmann distribution.

Laue group mm2

bears fooling around on a ladder

point group mm2

Sohncke group mmm

Copper

Silver

Gallium

Molybdenum

These species have the same ionic radius.

These species have the same net charge.

The statement is false, the form factor is independent of the element.

These species are isoelectronic.

they contain discrete molecules.

the arrangement of the chemical components in the crystal is periodic in 3 dimensions.

there are electrons present.

X-rays have a wavelength < 1 nm.

Kα₁

Kα₂

Kβ

Bremsstrahlung

only the major component.

only the minor component.

a mixture of the components in any ratio.

any of the above.

about 1.54 Å

exactly 0.71 Å

less than 0.54 Å

1.937 Å

h0l: h+l = 2n+1

h00: h = 2n

0k0: k = 2n+1

There are no systematic absences generated by this symmetry element.

a lattice

the concept of mosaicity

libration effects

plane group p1

the compound in the crystal is a single enantiomer and you have successfully determined its absolute configuration.

the compound in the crystal is a single enantiomer, but its absolute configuration cannot be determined   unambiguously.

you have a mixture of diastereoisomers.

the compound in the crystal is racemic and you have successfully determined the absolute structure (direction of the polar axis).

All reflections are allowed.

The sum of all hkl indices must be an even number.

The sum of all hkl indices must be an odd number.

hkl: h+k, k+l, h+l = 2n

general reflections

central reflections

axial reflections

zonal reflections

422

I4/m

mmm

$$\overline{4}$$

a = b = c, and all angles 90°.

three 4-fold axes in the diffraction pattern.

the vector [111] (space diagonal).

more than one 3-fold rotation axis.

a 90° unit cell angle can be achieved without changing the unit cell volume.

the lattice symmetry is higher than that of the corresponding P lattice.

the resulting unit cell volume doubles compared with the primitive unit cell.

the crystal system is tetragonal, trigonal, hexagonal or cubic.

cubic

orthorhombic

hexagonal

tetragonal

Dorothy Hodgkin (solved structures of penicillin and vitamin B12)

Rosalind Franklin (discovery of DNA was based on her work)

Isabella Karle (developed direct methods with her husband Jerome)

Queen Elizabeth II

a mirror plane not intersecting or coincident with a 2-fold axis.

a centre of inversion (always).

two mutually perpendicular mirror planes, both of which are parallel to a 2-fold axis.

two mutually perpendicular mirror planes, only one of which is parallel to a 2-fold axis.

Correct.

Incorrect.

It depends on the orientation of 2-fold axes.

This is not a proper point group.

 in the middle of every edge of the unit cell.

in the centre of every face of the unit cell.

at ½, ½, ½.

along the body diagonals of the unit cell.

∞/mmm (D∞_h)

Laue group 6/mmm

$$\overline{6}$$

cannot be assigned a point group

the crystal is an inversion twin.

the refinement model may be correct, but the Flack parameter is ambiguous.

the absolute structure cannot be determined.

You must invert your refinement model for the structure.

test for twinning.

calculate the atomic form factor.

compare intensities of equivalent reflections.

calculate the resolution of a reflection.

the crystal is an inversion twin.

you must invert your refinement model for the structure.

the refinement model is correct and needs no further refinement.

the refinement model may be correct, but the Flack parameter is ambiguous.

a single crystal.

a gas.

bee’s wax.

some polycrystalline material.

carbonyl oxygen atom

hydroxy oxygen atom

methyl group

fluorine atom

can and should always be prevented by changing the crystallization conditions.

should be resolved automatically by a special algorithm.

makes heavy atoms appear lighter in the difference Fourier map.

is characterized by a reciprocal or real space geometrical relationship between domains.

0°

0 - 360°

0 or 180°

0, 90, 180 or 270°

diffraction at long (red) and short (blue) wavelengths

diffraction at short (red) and long (blue) wavelengths

diffraction of neutrons and visible light

diffraction of electrons at high energy

the Bernoulli principle

the 18 electron rule

the 18 ų rule

The law of large numbers (LLN)

the number of formula units in the asymmetric unit

the number of formula units in the unit cell

the number of atoms in the unit cell

 the numbering of elements in the periodic table

It represents the symmetry of the X-ray diffraction pattern.

It is a prerequisite for systematic absences.

A higher symmetry Laue class makes it easier to determine the space group.

The Fourier synthesis requires knowledge of the Laue class.

a single crystal.

a twinned crystal.

probably glass.

a polycrystalline material.

the space group is incorrect.

the metal is really an element lighter than Ru.

the crystal quality is bad, which leads to Fourier ripples.

the absorption correction was faulty.

no birefringence along optic axis

crystal always polarizes the light

lamellar lines on crystal surfaces

split reflections

structure factors

direction of the reflection vectors

direction of the reflection vector and its intensity

reflection phases

2 2 4

1 1 4

2 1 1

1 1 2

6₃/mmc (centrosymmetric)

6/mmm (Laue group)

$$\overline{6}$$ (same as 3/m)

mmm

$$\sin^2\theta=\frac{4\lambda}{c^2}\left(h^2+k^2+l^2\right)$$

$$\sin^2\theta=\frac{\lambda^2}{4a^2}\left(h^2+k^2+l^2\right)$$

$$n^2\lambda^2=4d^2\sin^2\theta$$

$$\frac{1}{d^2}=\frac{h^2}{a^2\sin^2\beta}+\frac{k^2}{b^2}+\frac{l^2}{c^2\sin^2\beta}-\frac{2hl\cos\beta}{ac\sin^2\beta}$$

intensity

diffraction angle

unit cell constants

diffraction angle and relative intensity

constructive and destructive interference.

 diffraction of waves.

normal scattering of two waves.

a sine signal on an oscilloscope screen.

PDB

ICSD

PDF

CCDC

due to the low intensity of diffraction

because of the phase problem

because of long computation times

due to difficulties with crystal growing

X-ray, neutrons, microwaves

gamma rays, electrons, X-rays

X-ray, neutrons, electrons, synchrotron radiation

X-rays, UV, IR

Use Mo radiation with no restriction.

Use Cu radiation. Alternatively use Mo radiation and position the detector far from the sample.

No change is necessary if the crystal contains heavy elements.

Cu and Mo radiation are equally suitable for the experiment.

00l: l = 2n+1

00l: l ≠ 4n

00l: l = 4n

There are no systematic absences generated by this symmetry element.

cubic crystal system.

monoclinic crystal system.

triclinic crystal system.

trigonal crystal system in rhombohedral setting.

of heavy atom structures.

of light atom structures.

of any kind of structures.

only of centrosymmetric structures.

Cu

C

N

O

lower resolution.

higher resolution.

higher intensities.

higher intensities and resolution.

tens of kV.

12V.

230V AC.

1000V.

SONY full frame camera

digital detector with direct readout

photographic film

proportional counter

$$\left(210\right)$$ or $$\left(\overline{2}\overline{1}0\right)$$

$$\left(210\right)$$

$$\left(120\right)$$

$$\left(\overline{12}0\right)$$

generating high intensity radiation in the synchrotron.

collimating and focusing the primary beam.

filtering Bremsstrahlung.

accelerating electrons.

phases

intensities

scattering power

phases and Miller indeces

reduces resolution.

reduces the data collection time.

improves diffraction strength of the crystal.

all of the above

filtered radiation.

electrons.

non-monochromatic radiation.

incoherent radiation.

Miller indices.

the θ angle.

the 2θ angle.

structure factors.

completely eliminate Kβ.

eliminate Kα₁ and Kα₂.

eliminate Bremsstrahlung.

eliminate Bremsstrahlung and Kα₁ / Kα₂.

diffraction peaks on maps of electron density.

the distribution of electron density in the unit cell.

general intensity scattering.

intensities of the peaks and phase distribution over time.

90°

180°

120°

100°

by using short wavelength radiation

by using smaller crystals with a near-isotropic shape

by properly mounting and centering the sample

all of the above

heating

cooling or applying high pressure

leave the crystals undisturbed for a long time, to allow the molecules to organize themselves

none of the above

phases and intensities

only intensities

phases and directions

all of the above